Stan, lists, Thanks for your thought-provoking comments about the possible role of environment in organization.
(1) I am glad that we agree that the vertical hierarchy in Figure 1 is a *compositional* hierarchy. This hierarchy seems to have two more characteristics -- (i) The *scale* of measurement increasing from angstroms to light years from bottom to top (and hence it may be referred to as a *scale hierarchy* as well), and (ii) the degree of the *organized complexity* (and not necessarily the disorganized complexity of Weaver [8]) is increasing from the bottom to the top. (2) It is interesting to note that there does not seem to be any obvious* hierarchical relations* among the objects belonging to a given level. (3) To the best of my knowledge, there is no generally accepted mathematical equation yet that can quantify *organization *or *organized complexity *of Weaver. But *disorganized *or* random complexity* can be quantified using the algorithmic (or Kolmogorov) complexity measure (e.g., [9]), which is maximal for random complex systems. Although I have not yet proven the idea, it seems possible to quantify the degree of organization of a physical system using the *Planckian distribution equation (PDE)* discovered at Rutgers in 2008 and discussed rather in depth last November in the Peirce-L and [biosemiotics] lists [10] (which I would be happy to forward to anyone interested). If this conjecture turns out to be correct, it would be possible to state that the *Planckian information*, I_P, increases from the bottom to the top in Figure 1. With all the best. Sung _____________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net On Sun, Sep 13, 2015 at 10:19 AM, Stanley N Salthe <[email protected]> wrote: > Sung’s hierarchy: > > > 9. * Universe *(our Universe, other universes; > *Cosmology*) > > ^ > > | > > | > > 8. *Galaxy* (Milky Way, other galaxies; ' > *Galaxology*') > > ^ > > | > > | > > 7. * Planet *(Earth, other planets; *Planetology*) > > ^ > > | > > | > > 6. *Biosphere* (unique ?; *Ecology*) > > ^ > > | > > | > > 5. *Societies* (ants, bees, humans, . . . ; > *Sociology*) > > ^ > > | > > | > > 4. * Brains* (bees, apes, humans, . . .; > *Psychology*) > > ^ > > | > > | > > 3. *Cells* (bacteria, yeast, white blood cells, > . . .;*Biology*) > > ^ > > | > > | > > 2. *Molecules* (water, sugar, DNA, hemoglobin, . . > .;*Chemistry*) > > ^ > > | > > | > > 1. *Atoms* (hydrogen, oxygen, nitrogen, . . .; > *Physics*) > > > > *Figure 1.* Nine levels of material ORGANIZATION with associated EMERGENT > properties. > > -------------------------------- > > is indeed a compositional hierarchy > > He shows it as if being built from the bottom-up, each level emergent from > the one below. But there are important constraints on what appears at any > level simultaneously imposed top-down. This means that the beginning had > to be somewhere, and that somewhere somehow afforded the lowest level. In > addition, that somewhere continues to exist at the top as the hierarchy > gets built, by intercalation between levels. Thus, take Molecules. They > emerge from attractions of various kinds working upon the atoms subject to > environmental constraints that allow this to happen. These will have been > imposing an environment later taken over by Cells. Then, consider Brains. > These multicellular forms emerge by way of cell adhesions in a contextual > environment, which later affords the intercalation of societies of > organisms. That is, there would have been environmental constraints that > later would have been built upon to form the societies listed. > > BUT, this kind of hierarchy is not usually used to represent evolution, or > change. Rather one looks at Sung’s chart and sees the current situation, > but it needs the addition of top-down constraints (restrictive and > enabling) working at each level. Thus, in his picture, you have brains > because cells found themselves in a social-like situation, and you have > molecules because atoms found themselves in a situation imposing > constraints like those that a cell imposes internally. > > Regarding (4), invoking subsumption for the simple {type {token}} > relationship is on the face of it a bit of overkill. No actual hierarchies > are shown at each level. > > The rest looks OK to me. > > STAN > > On Sat, Sep 12, 2015 at 9:21 PM, Sungchul Ji <[email protected]> wrote: > >> Hi, >> >> >> I modified and expanded the *structural hierarchy* discussed in >> [biosemiotics:8854] to include 4 more levels -- biosphere, the earth, >> galaxy, and the Universe as shown *Figure 1* below. >> >> >> (1) The *structural hierarchy* consists of 9 levels, numbered 1 through >> 9, each, except perhaps Level 6, having more than one members or examples >> belonging to it as shown in the parenthesis. >> >> (2) Each level can be identified as a *type* and the members belonging >> to it as its *tokens*. Hence all the items in the network can be >> symbolically represented as T_i or as T_i,j, where i is the level and j is >> the number identifying the members belonging to the i^th level. >> >> (3) The symbol, "A ---> B", can be read as "A is a part of B" and hence >> Figure 1 can be called "*compositional hierarchy*" [1]. >> >> (4) Each level constitutes a "subsumption hierarchy" [1], since what is >> inside a parenthesis can be viewed as "*a kind of*" something", the >> "something" being the name of the level, e.g., Atom, Molecule, Cell, etc. >> That is, "Oxygen is a kind of Atom", "Hydrogen is a kind of Atom," >> "Nitrogen is a kind of Atom.", etc. Using the symbols defined in (2), we >> can more succinctly write, "T_i,j is *a kind of* T_i". >> >> (5) Each level is associated with a unique "discipline" (see the terms >> in bold letters), and this "discipline", I suggest, can be identified with >> what is called "*functors*"in category theory [2, 3], since it provides >> the connection among the "structure-preserving mappings" or "*morphisms*" >> that in turn connect the members belonging to a given discipline. >> >> (6) If the the category-theoretical assignments assumed in (5) are >> correct, there are 8 (if Level 6 is excluded) or 9 (if not) *functors* >> in the structural hierarchy shown in Figure 1. The *structure-preserving >> mapping* that connects one functor to another is known as a *natural >> transformation* [2, 4]. >> >> (7) I postulate that the natural transformation connecting the 8 or 9 >> functors in Figure 1 is *organization *(i.e., the arrangement of >> particles or symbols in space and time). >> >> (8) Finally, according to the *Gnergy Principle of Organization* (GPO) >> [5, 6, 7], all organizations in the Universe, including both biotic and >> abiotic systems, have two complementary aspects -- *informational* (or >> formal) and *energetic* (or material) aspects. In other words, if GPO is >> true, no organization of matter in the Universe would be possible without >> the *energy* dissipation driving the performance of the work of >> organizing and the *information* to guide the work, since any work >> without being guided by appropriate control information would inevitably >> lead to "*disorganized*" complexity [8]. >> >> >> >> >> >> 9. * Universe *(our Universe, other universes; >> *Cosmology*) >> ^ >> | >> | >> 8. *Galaxy* (Milky Way, other galaxies; ' >> *Galaxology*') >> ^ >> | >> | >> 7. * Planet *(Earth, other planets; *Planetology*) >> ^ >> | >> | >> 6. *Biosphere* (unique ?; *Ecology*) >> ^ >> | >> | >> 5. *Societies* (ants, bees, humans, . . . ; *Sociology*) >> >> ^ >> | >> | >> 4. * Brains* (bees, apes, humans, . . .; *Psychology*) >> ^ >> | >> | >> 3. *Cells* (bacteria, yeast, white blood cells, . . >> .; *Biology*) >> ^ >> | >> | >> 2. *Molecules* (water, sugar, DNA, hemoglobin, . . .; >> *Chemistry*) >> ^ >> | >> | >> 1. *Atoms* (hydrogen, oxygen, nitrogen, . . .; >> *Physics*) >> >> *Figure 1.* Nine levels of material ORGANIZATION with associated >> EMERGENT properties. >> Reproduced and modified from [biosemiotics:8854]. >> >> >> If you have any comments or questions, let me know. >> >> With all the best. >> >> >> Sung >> -- >> Sungchul Ji, Ph.D. >> >> Associate Professor of Pharmacology and Toxicology >> Department of Pharmacology and Toxicology >> Ernest Mario School of Pharmacy >> Rutgers University >> Piscataway, N.J. 08855 >> 732-445-4701 >> >> www.conformon.net >> >> >> *References:* >> [1] Salthe, S. N. (20xx). Hierarchical Structures. *Axiomathes* >> Where Science Meets Philosophy* 22*:355-383. >> [2] Spivak, D. I. (2013). Category Theory for Scientists. >> http://math.mit.edu/~dspivak/teaching/sp13/CT4S--static.pdf >> [3] Brown, R. and Porter, T. (20xx). Category Theory: an abstract >> setting for analogy and comparison. >> http://pages.bangor.ac.uk/~mas010/Analogy-and-Comparison.pdf >> [4] Natural Transformation. >> https://en.wikipedia.org/wiki/Natural_transformation >> [5] Ji, S. (1991). Biocybernetics: A Machine Theory of Biology,* in* >> *Molecular >> Theories of * >> *Cell Life and Death, *S. Ji (ed.), Rutgers University Press, New >> Brunswick, pp. 1-237. >> [6] Ji, S. (2004). Semiotics of Life: A Unified Theory of Molecular >> Machines, Cells, the >> Mind, Peircean Signs, and the Universe Based on the Principle of >> Information-Energy Complementarity, >> in: Reports, Research Group on Mathematical >> *Linguistics, XVII Tarragona Seminar on Formal Syntax and Semantics,*Rovira >> i Virgili University, Tarragona, Spain, April 23-27, 2003. Available at >> http://grammars.grlmc.com/GRLMC/reports/ or at http://www.conformon.net >> under Publications > >> Proceedings and Abstracts. >> [7] Ji, S. (2012). Complementarity. >> <http://www.conformon.net/wp-content/uploads/2012/08/Excerpts_Chapters_2_complementarity_08192012.pdf> >> In: >> *Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, **and >> Biomedical Applications.* Springer, New York. Section 2.3, pp. 24-50. >> PDF at http://www.conformon.net >> [8] Weaver, W. (1948). Science and Complexity. *Am. Scientist*. >> *36*:536. Down loaded from >> >> http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L1/Material/WEAVER1947.pdf >> on 9/12/2015. >> > [9] Mikhailovsk, G. E. and Levich, A. P. (2015). Entropy, Information and Complexity or Which Aims the Arrow of Time ? *Entropy* *17*: 4863-4890; doi:10.3390/e17074863. [10] Ji, S. (2014). A quantitative model of organization called PITO (Planckian Information Theory of Organization). [PEIRCE-L] post dated 11/2/1014. > >> >> >> >
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